The dual of Bergman metric VMO (Q1567152)

The main result of this paper is a new proof of the theorem which says that the dual of the Bergman metric \(\text{VMO}_p\) is the space \(H^1_q\) consisting of \(\ell^1\)-sums of Bergman metric \(q\)-atoms \(({1\over p}+{1\over q}= 1)\) and moreover that the second dual is \(\text{BMO}_p\). Very interesting are also parts 3 and 4 were among others we have the theorem that the continuous functions on \(D\cup\partial D\) are dense in \(\text{VMO}_p\) (Remark 3.6) and \(L_h= \sum\overline\lambda_g L_g\), where \(h= \sum \lambda_g g\in H^1_q\) and \(f\in \text{BMO}_p\) (Theorem 4.1).